非线性弹性基础上矩形板热后屈曲分析

给出非线性弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下的后屈曲分析。采用摄动——Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。数值计算结果表明，非线性弹性基础上矩形板具有不稳定的热后屈曲平衡路径，且对初始几何缺陷是敏感的     

Laminar mixed convection on a horizontal plate of finite length in a channel of finite width

The steady two-dimensional laminar mixed-convection flow past a horizontal plate of finite length is analysed for large Péclet numbers, small Prandtl numbers and weak buoyancy effects. The plate is placed in a channel of finite width, with the plane walls of the channel being parallel to the plate. The temperature of the plate is assumed to be constant. The hydrostatic pressure difference across the wake behind the plate is compensated by a perturbation of the inviscid channel flow. This outer flow perturbation affects the temperature distribution in the thermal boundary layer at the plate and the heat transfer rate, respectively. Solutions in closed form are given. The forces acting on the plate due to the potential flow perturbation are also determined.     

Analysis of the transpiration cooling of a thin porous plate in a hot laminar convective flow

This paper deals with the asymptotic and numerical analysis for the steady-state transpiration cooling of a thin porous flat plate in a laminar hot convective flow, taking into account the streamwise heat conduction through the plate. For high conductivity plates, a regular perturbation analysis has been carried out, yielding a three-term asymptotic solution for the distribution of plate temperature. In the limit of a very poorly conducting plate, a singular perturbation technique, based on matched asymptotic expansions, is employed to solve the governing equations. We also solved the equations numerically using a quasilinearization technique. The numerical results are in good agreement with the asymptotic solution close to the asymptotic limits studied.     

On the analysis of a plate with a local shape perturbation

The asymptotic behavior of the solution of the bending problem of plates with local shape perturbations (connections, ribs, holes comparable in size with the plate thickness) is studied in a three-dimensional formulation using the local perturbation method. The problem is completely decomposed into a two-dimensional problem of plate theory and local problems describing the threedimensional stress-strain state in the perturbation region. The local problems are solved using numerical methods.     

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is co…     

ON SOLVING HIGH-ORDER SOLUTIONS OF CHIEN’S PERTURBATION METHOD TO STUDY CONVERGENCE BY COMPUTER

In this paper, we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation. All unkown constants of every perturbation solution can be determined by computer. Hence higher order perturbation solution is obtained. Based on the solution of higher order perturbation, asymptotical property and suitable interval of Chien’s perturbation method are also discussed.     

Improvements on the arc-length-type method

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods. The project supported by the Special Research Fund for Doctor Program of Universities (9424702)     

高频吹气扰动影响近壁区拟序结构统计特性的实验研究

利用恒温热线风速仪测量了零压力梯度平板上施加由合成射流激发的狭缝周期吹气扰动前后不同流向位置湍流边界层的速度信号, 展开高频吹气扰动影响近壁区湍流结构的统计特性研究. 研究结果表明:高频周期吹气扰动在狭缝下游产生明显的减阻效果. 扰动强度在湍流边界层内的发展沿流向呈衰减趋势, 其与湍流结构的相互作用也相应衰减. 然而, 因高频扰动产生运动的展向涡结构与猝发引起的结构变化尺度相当, 直接影响了近壁区拟序结构产生与发展的统计, 从而使得猝发检测方法VITA 表现出与低频或定常吹气减阻机理相异的现象.      

The perturbation parameter in the problem of large deflection of clamped circular plates

In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads. This paper is completed under the guidance of Prof. Chien Wei-zang.     

Thermal postbuckling analysis of moderately thick plates

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.     

Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate

This paper presents the study on the chaotic wave and chaotic dynamics of the nonlinear wave equations for a simply supported truss core sandwich plate combined with the transverse and in-plane excitations. Based on the governing equation of motion for the simply supported sandwich plate with truss core, the reductive perturbation method is used to simplify the partial differential equation. According to the exact solution of the unperturbed equation, two different kinds of the topological structures are derived, which one structure is the resonant torus and another structure is the heteroclinic orbit. The characteristic of the singular points in the neighborhood of the resonant torus for the nonlinear wave equation is investigated. It is found that there exists the homoclinic orbit on the unperturbed slow manifold. The saddle-focus type of the singular point appears when the homoclinic orbit is broken under the perturbation. Additionally, the saddle-focus type of the singular point occurs when the resonant torus on the fast manifold is broken under the perturbation. It is known that the dynamic characteristics are well consistent on the fast and slow manifolds under the condition of the perturbation. The Melnikov method, which is called the first measure, is applied to study the persistence of the heteroclinic orbit in the perturbed equation. The geometric analysis, which is named the second measure, is used to guarantee that the heteroclinic orbit on the fast manifold comes back to the stable manifold of the saddle on the slow manifold under the perturbation. The theoretical analysis suggests that there is the chaos for the Smale horseshoe sense in the truss core sandwich plate. Numerical simulations are performed to further verify the existence of the chaotic wave and chaotic motions in the nonlinear wave equation. The damping coefficient is considered as the controlling parameter to study the effect on the propagation property of the nonlinear wave in the sandwich plate with truss core. The numerical results confirm the validity of the theoretical study.     

Nonlinear three-dimension analysis for axially symmetrical circular plates and multilayered plates

Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearily from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective.     

变厚度中厚板和中厚壳的大挠度分析

采用摄动有限元法分析了变厚度中厚板和中厚壳的大挠度问题。文中借助虚功原理导出了这类板壳的一般非线性有限元方程，同时利用摄动展开求得了逐级摄动有限元的递推算式。算例表明，摄动有限元法分析变厚度中厚板壳问题同样能获得效率高精度好的结果。     

Streamwise vibrations of a plate in a viscous fluid flow in a channel,induced by forced transverse vibrations of the plate

Aeroelastic vibrations of a plate aligned at a zero angle of attack in a viscous incompressible fluid flow in a channel with parallel walls are considered within the framework of a plane model. Forced vibrations of the plate in the transverse direction give rise an unsteady component of the flow friction force, induced by the perturbation of the fluid flow velocity by the vibrating plate. Under the assumption of the laminar character of the fluid flow, it is demonstrated that this force can excite streamwise vibrations of the plate if the channel width is small as compared with the plate length; these streamwise vibrations have the same order as the transverse vibrations of the plate excited by external forces.     

复合材料层合板的三维研究

本文提出了固支复合材料各向异性层合圆板受均布横向载荷作用下的满足三维弹性力学基本微分方程和边界条件的解析解答。文中采用一种发展的摄动方法进行求解，板中的每个应力和位移都展开为无量纲厚度参数ε的摄动级数，并采用二维板理论解答作为其相应三维摄动解答的一个基本解的形式，通过摄动方法逐级求解而获得完整的三维解答。文中以解析形式和数值形式给出了高精确度的三维应力和位移结果，结果表明，本文求解三维问题的解析方法是合理有效的。     

双参数弹性地基上圆板的轴对称大挠度问题

提出将摄动法和积分方程法联合应用于Ｐａｓｔｅｒｎａｋ弹性地基上圆板的轴对称大挠度问题。该方法简明、计算量小、结果可靠。     

Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source in a nanofluid

The unsteady magnetohydrodynamic flow of a nanofluid past an oscillatory moving vertical permeable semi-infinite flat plate with constant heat source in a rotating frame of reference is theoretically investigated. The velocity along the plate (slip velocity) is assumed to oscillate on time with a constant frequency. The analytical solutions of the boundary layer equations are assumed of oscillatory type and they are obtained by using the small perturbation approximations. The influence of various relevant physical characteristics are presented and discussed.     

小内力平板弹性波散射问题的摄动方法

基于平板小挠度弯曲波动方程,采用摄动方法具有纵向内力作用下的平板开孔弹性波的散射问题进行了研究,得么了传播稳态波时此种平板弯曲波动问题的分析解,分析了均匀纵向内力对弹性波散射结果的影响,作为算例,本文给出了平板圆形开孔的动应力集中系数的数值结果,并对计算结果进行了讨论。     

具有随机路径的振动传递路径系统的随机响应分析

基于一般概率摄动有限元法,解决了具有随机路径的振动传递路径系统的响应分析问题.应用Kronecker代数,矩阵微分理论,向量值和矩阵值函数的二阶矩技术,矩阵摄动理论和概率统计方法,提出了振动传递路径系统的随机响应分析方法,在考虑工程中的不确定因素以后,在时域内清晰地描述了振动传递路径的随机响应.     

Energy functional derivative with respect to the length of a curvilinear oblique cut in the equilibrium problem for a Timoshenko plate

This paper describes the dependence of the solution of the equilibrium problem for a Timoshenko plate and the total energy functional of the plate on the perturbation of an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which describe mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.